Question

find the difference quotient of f, that is, find $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, for the following function. be sure to simplify.
f(x) = x^2 - 4x + 5
$\frac{f(x + h)-f(x)}{h}=$

Explanation:

Step1: Find $f(x + h)$

$f(x+h)=(x + h)^2-4(x + h)+5=x^{2}+2xh+h^{2}-4x-4h + 5$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(x^{2}+2xh+h^{2}-4x-4h + 5)-(x^{2}-4x + 5)=2xh+h^{2}-4h$

Step3: Find the difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{2xh+h^{2}-4h}{h}=2x + h - 4$

Answer:

$2x + h - 4$